Method for reduced bit-depth quantization

ABSTRACT

A method is provided for the quantization of a coefficient. The method comprises: supplying a coefficient K; supplying a quantization parameter (QP); forming a quantization value (L) from the coefficient K using a mantissa portion (Am)(QP)) and an exponential portion (x Ae(QP) ). Typically, the value of x is 2. In some aspects of the method, forming a quantization value (L) from the coefficient K includes L=K*A(QP)=K*Am(QP)*(2 Ae(QP) ). In other aspects, the method further comprises: normalizing the quantization value by 2 N  as follows: Ln=L/2 N =K*Am(QP)/2 (N-Ae(QP)) . In some aspects, forming a quantization value includes forming a set of recursive quantization factors with a period P, where A(QP+P)=A(QP)/x. Forming recursive quantization factors includes forming recursive mantissa factors, where Am(QP)=Am(QP mod P), and forming recursive quantization factors includes forming recursive exponential factors, where Ae(QP)=Ae(QP mod P)−QP/P.

RELATED APPLICATIONS

[0001] This application claims the benefit of a provisional application entitled, REDUCED BIT-DEPTH QUANTIZATION, invented by Louis Kerofsky, Ser. No. 06/311,436, filed Aug. 9, 2001, attorney docket no. SLA1110P.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] This invention generally relates to video compression techniques and, more particularly, to a method for reducing the bit size required in the computation of video coding transformations.

[0004] 2. Description of the Related Art

[0005] A video information format provides visual information suitable to activate a television screen, or store on a video tape. Generally, video data is organized in a hierarchical order. A video sequence is divided into group of frames, and each group can be composed of a series of single frames. Each frame is roughly equivalent to a still picture, with the still pictures being updated often enough to simulate a presentation of continuous motion. A frame is further divided into slices, or horizontal sections which helps system design of error resilience. Each slice is coded independently so that errors do not propagate across slices. A slice consists of macroblocks. In H.26P and Motion Picture Experts Group (MPEG)-X standards, a macroblock is made up of 16×16 luma pixels and a corresponding set of chroma pixels, depending on the video format. A macroblock always has an integer number of blocks, with the 8×8 pixel matrix being the smallest coding unit.

[0006] Video compression is a critical component for any application which requires transmission or storage of video data. Compression techniques compensate for motion by reusing stored information in different areas of the frame (temporal redundancy). Compression also occurs by transforming data in the spatial domain to the frequency domain. Hybrid digital video compression, exploiting temporal redundancy by motion compensation and spatial redundancy by transformation, such as Discrete Cosine Transform (DCT), has been adapted in H.26P and MPEG-X international standards as the basis.

[0007] As stated in U.S. Pat. No. 6,317,767 (Wang), DCT and inverse discrete cosine transform (IDCT) are widely used operations in the signal processing of image data. Both are used, for example, in the international standards for moving picture video compression put forth by the MPEG. DCT has certain properties that produce simplified and efficient coding models. When applied to a matrix of pixel data, the DCT is a method of decomposing a block of data into a weighted sum of spatial frequencies, or DCT coefficients. Conversely, the IDCT is used to transform a matrix of DCT coefficients back to pixel data.

[0008] Digital video (DV) codecs are one example of a device using a DCT-based data compression method. In the blocking stage, the image frame is divided into N by N blocks of pixel information including, for example, brightness and color data for each pixel. A common block size is eight pixels horizontally by eight pixels vertically. The pixel blocks are then “shuffled” so that several blocks from different portions of the image are grouped together. Shuffling enhances the uniformity of image quality.

[0009] Different fields are recorded at different time incidents. For each block of pixel data, a motion detector looks for the difference between two fields of a frame. The motion information is sent to the next processing stage. In the next stage, pixel information is transformed using a DCT. An 8-8 DCT, for example, takes eight inputs and returns eight outputs in both vertical and horizontal directions. The resulting DCT coefficients are then weighted by multiplying each block of DCT coefficients by weighting constants.

[0010] The weighted DCT coefficients are quantized in the next stage. Quantization rounds off each DCT coefficient within a certain range of values to be the same number. Quantizing tends to set the higher frequency components of the frequency matrix to zero, resulting in much less data to be stored. Since the human eye is most sensitive to lower frequencies, however, very little perceptible image quality is lost by this stage.

[0011] The quantization stage includes converting the two-dimensional matrix of quantized coefficients to a one-dimensional linear stream of data by reading the matrix values in a zigzag pattern and dividing the one-dimensional linear stream of quantized coefficients into segments, where each segment consists of a string of zero coefficients followed by a non-zero quantized coefficient. Variable length coding (VLC) then is performed by transforming each segment, consisting of the number of zero coefficients and the amplitude of the non-zero coefficient in the segment, into a variable length codeword. Finally, a framing process packs every 30 blocks of variable length coded quantized coefficients into five fixed-length synchronization blocks.

[0012] Decoding is essentially the reverse of the encoding process described above. The digital stream is first deframed. Variable length decoding (VLD) then unpacks the data so that it may be restored to the individual coefficients. After inverse quantizing the coefficients, inverse weighting and an inverse discrete cosine transform (EDCT) are applied to the result. The inverse weights are the multiplicative inverses of the weights that were applied in the encoding process. The output of the inverse weighting function is then processed by the IDCT.

[0013] Much work has been done studying means of reducing the complexity in the calculation of DCT and IDCT. Algorithms that compute two-dimensional IDCTs are called “type I” algorithms. Type I algorithms are easy to implement on a parallel machine, that is, a computer formed of a plurality of processors operating simultaneously in parallel. For example, when using N parallel processors to perform a matrix multiplication on N×N matrices, N column multiplies can be simultaneously performed. Additionally, a parallel machine can be designed so as to contain special hardware or software instructions for performing fast matrix transposition.

[0014] One disadvantage of type I algorithms is that more multiplications are needed. The computation sequence of type I algorithms involves two matrix multiplies separated by a matrix transposition which, if N=4, for example, requires 64 additions and 48 multiplications for a total number of 112 instructions. It is well known by those skilled in the art that multiplications are very time-consuming for processors to perform and that system performance is often optimized by reducing the number of multiplications performed.

[0015] A two-dimensional IDCT can also be obtained by converting the transpose of the input matrix into a one-dimensional vector using an L function. Next, the tensor product of constant a matrix is obtained. The tensor product is then multiplied by the one-dimensional vector L. The result is converted back into an N×N matrix using the M function. Assuming again that N=4, the total number of instructions used by this computational sequence is 92 instructions (68 additions and 24 multiplications). Algorithms that perform two-dimensional EDCTs using this computational sequence are called “type II” algorithms. In type II algorithms, the two constant matrices are grouped together and performed as one operation. The advantage of type II algorithms is that they typically require fewer instructions (92 versus 112) and, in particular, fewer costly multiplications (24 versus 48). Type II algorithms, however, are very difficult to implement efficiently on a parallel machine. Type II algorithms tend to reorder the data very frequently and reordering data on a parallel machine is very time-intensive.

[0016] There exist numerous type I and type II algorithms for implementing IDCTs, however, dequantization has been treated as an independent step depending upon DCT and IDCT calculations. Efforts to provide bit exact DCT and IDCT definitions have led to the development of efficient integer transforms. These integer transforms typically increase the dynamic range of the calculations. As a result, the implementation of these algorithms requires processing and storing data that consists of more than 16 bits.

[0017] It would be advantageous if intermediate stage quantized coefficients could be limited to a maximum size in DCT processes.

[0018] It would be advantageous if a quantization process could be developed that was useful for 16-bit processors.

[0019] It would be advantageous if a decoder implementation, dequantization, and inverse DCT could be implemented efficiently with a 16-bit processor. Likewise, it would be advantageous if the multiplication could be preformed with no more than 16 bits, and if memory access required no more than 16 bits.

SUMMARY OF THE INVENTION

[0020] The present invention is an improved process for video compression. Typical video coding algorithms predict one frame from previously coded frames. The error is subjected to a transform and the resulting values are quantized. The quantizer controls the degree of compression. The quantizer controls the amount of information used to represent the video and the quality of the reconstruction.

[0021] The problem is the interaction of the transform and quantization in video coding. In the past the transform and quantizer have been designed independently. The transform, typically the discrete cosine transform, is normalized. The result of the transform is quantized in standard ways using scalar or vector quantization. In prior work, MPEG-1, MPEG-2, MPEG-4, H.261, H.263, the definition of the inverse transform has not been bit exact. This allows the implementer some freedom to select a transform algorithm suitable for their platform. A drawback of this approach is the potential for encoder/decoder mismatch damaging the prediction loop. To solve this mismatch problem portions of the image are periodically coded without prediction. Current work, for example H.26L, has focused on using integer transforms that allow bit exact definition. Integer transforms may not normalized. The transform is designed so that a final shift can be used to normalize the results of the calculation rather than intermediate divisions. Quantization also requires division. H.26L provides an example of how these integer transforms are used along with quantization.

[0022] In the current H.26L Test Model Long-term (TML), normalization is combined with quantization and implemented via integer multiplications and shifts following forward transform and quantization and following dequantization and inverse transform. H.26L TML uses two arrays of integers A[QP] and B[QP] index by quantization parameter, see Table 1. These values are constrained by the relation shown below in Equation 1. TABL3 1 TML quantization parameters Qp A-TML B-TML 0 620 3881 1 553 4351 2 492 4890 3 439 5481 4 391 6154 5 348 6914 6 310 7761 7 276 8718 8 246 9781 9 219 10987 10 195 12339 11 174 13828 12 155 15523 13 138 17435 14 123 19561 15 110 21873 16 98 24552 17 87 27656 18 78 30847 19 69 34870 20 62 38807 21 55 43747 22 49 49103 23 44 54683 24 39 61694 25 35 68745 26 31 77615 27 27 89113 28 24 100253 29 22 109366 30 19 126635 31 17 141533

Equation 1 Joint Normalization/Quantization Relation

A(QP)·B(QP)·676²≈2⁴⁰.

[0023] Normalization and quantization are performed simultaneously using these integers and divisions by powers of 2. Transform coding in H.26L uses a 4×4 block size and an integer transform matrix T, Equation 2. For a 4×4 block X, the transform coefficients K are calculated as in Equation 3. From the transform coefficients, the quantization levels, L, are calculated by integer multiplication. At the decoder the levels are used to calculate a new set of coefficients, K′. Additional integer matrix transforms followed by a shift are used to calculate the reconstructed values X′. The encoder is allowed freedom in calculation and rounding of the forward transform. Both encoder and decoder must compute exactly the same answer for the inverse calculations. $\begin{matrix} {\quad {{H{.26}L\quad {transform}\quad {matrix}}{T = \begin{pmatrix} 13 & 13 & 13 & 13 \\ 17 & 7 & {- 7} & {- 17} \\ 13 & {- 13} & {- 13} & 13 \\ 7 & {- 17} & 17 & {- 7} \end{pmatrix}}}} & \text{Equation~~2} \end{matrix}$

Equation 3 TML DCT_LUMA and iDCT_LUMA

Y=T·X

K=Y·T ^(T)

L=(A _(TML)(QP)·K)/2²⁰

K′=B _(TML)(QP)·L

Y′=T ^(T) ·K′

X′=(Y′·T)/2²⁰

[0024] The dynamic range required during these calculations can be determined. The primary application involves 9-bit input, 8 bits plus sign, the dynamic range required by intermediate registers and memory accesses is presented in Table 2. TABLE 2 Dynamic range of TML decoder (bits) 9-bit input DCT_LUMA iDCT_LUMA Register 30 27 Memory 21 26

[0025] To maintain bit-exact definitions and incorporate quantization, the dynamic range of intermediate results can be large since division operations are postponed. The present invention combines quantization and normalization, to eliminate the growth of dynamic range of intermediate results. With the present invention the advantages of bit exact inverse transform and quantization definitions are kept, while controlling the bit depth required for these calculations. Reducing the required bit depth reduces the complexity required of a hardware implementation and enables efficient use of single instruction multiple data (SIMD) operations, such as the Intel MMX instruction set.

[0026] Accordingly, a method is provided for the quantization of a coefficient. The method comprises: supplying a coefficient K; supplying a quantization parameter (QP); forming a quantization value (L) from the coefficient K using a mantissa portion (Am)(QP)) and an exponential portion (x^(Ae(QP))). Typically, the value of x is 2.

[0027] In some aspects of the method, forming a quantization value (L) from the coefficient K includes: L = K * A(QP) = K * Am(QP) * (2^(Ae(QP))).

[0028] In other aspects, the method further comprises: normalizing the quantization value by 2^(N) as follows: ${Ln} = {\frac{L}{2^{N}} = {K*{Am}{\frac{({QP})}{2^{({N - {{Ae}{({QP})}}})}}.}}}$

[0029] In some aspects, forming a quantization value includes forming a set of recursive quantization factors with a period P, where A(QP+P)=A(QP)/x. Therefore, forming a set of recursive quantization factors includes forming recursive mantissa factors, where Am(QP)=Am(QP mod P). Likewise, forming a set of recursive quantization factors includes forming recursive exponential factors, where Ae(QP)=Ae(QP mod P)−QP/P.

[0030] More specifically, supplying a coefficient K includes supplying a coefficient matrix K[i][j]. Then, forming a quantization value (L) from the coefficient matrix K[i][j] includes forming a quantization value matrix (L[i][j]) using a mantissa portion matrix (Am(QP)[i][j]) and an exponential portion matrix (x^(Ae(QP)[i][j])).

[0031] Likewise, forming a quantization value matrix (L[i][j]) using a mantissa portion matrix (Am(QP)[i][j]) and an exponential portion matrix (x^(Ae(QP)[i][j])) includes, for each particular value of QP, every element in the exponential portion matrix being the same value. Every element in the exponential portion matrix is the same value for a period (P) of QP values, where Ae(QP)=Ae(P*(QP/P)).

[0032] Additional details of the above-described method, including a method for forming a dequantization value (X1), from the quantization value, using a mantissa portion (Bm)(QP)) and an exponential portion (x^(Be(QP))), are provided below.

BRIEF DESCRIPTION OF THE DRAWINGS

[0033]FIG. 1 is a flowchart illustrating the present invention method for the quantization of a coefficient.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0034] The dynamic range requirements of the combined transform and quantization is reduced by factoring the quantization parameters A(QP) and B(QP) into a mantissa and exponent terms as shown in Equation 4. With this structure, only the precision due to the mantissa term needs to be preserved during calculation. The exponent term can be included in the final normalization shift. This is illustrated in the sample calculation Equation 5.

Equation 4 Structure of Quantization Parameters

A _(proposed)(QP)=A _(mantissa)(QP)·2^(A) ^(_(exponent)) ^((QP))

B _(proposed)(QP)=B _(mantissa)(QP)·2^(B) ^(_(exponent)) ^((QP))

Equation 5 Reduced Bit_depth DCT_LUMA

Y=T·X

K=Y·T ^(T)

L=(A _(mantissa)(QP)·K)/2^(20-A) ^(_(exponent)) ^((QP))

K′=T ^(T) ·L

Y′=K′·T

X′=(B _(mantissa)(QP)·Y′)/2^(20-B) ^(_(exponent)) ^((QP))

[0035] To illustrate the present invention, a set of quantization parameters is presented that reduce the dynamic range requirement of an H.26L decoder to 16-bit memory access. The memory access of the iDCT is reduced to 16 bits. Six pairs are defined (A, B) for QP=0-5, Table 3. Additional values are determined by recursion, Equation 6. The structure of these values makes it possible to generate new quantization values in addition to those specified. TABLE 3 Quantization values 0-5 for TML QP A_(mantissa) A_(exponent) B_(mantissa) B_(exponent) A_(proposed) B_(proposed) 0 5 7 235 4 640 3760 1 9 6 261 4 576 4176 2 127 2 37 7 508 4736 3 114 2 165 5 456 5280 4 25 4 47 7 400 6016 5 87 2 27 8 348 6912

Equation 6 Recursion Relations  A _(mantissa)(QP+6)=A _(mantissa)(QP)

B _(mantissa)(QP+6)=B _(mantissa)(QP)

A _(exponent)(QP+6)=A _(exponent)(QP)−1

B _(exponent)(QP+6)=B _(exponent)(QP)+1

[0036] Using the defined parameters, the DCT calculations can be modified to reduce the dynamic range as shown in Equation 5. Note how only the mantissa values contribute to the growth of dynamic range. The exponent factors are incorporated into the final normalization and do not impact the dynamic range of intermediate results.

[0037] With these values and computational method, the dynamic range at the decoder is reduced so only 16-bit memory access is needed as seen in Table 4. TABLE 4 Dynamic range with low-bit depth quantization (QP > 6) 8-bit DCT_LUMA iDCT_LUMA Register 28 24 Memory 21 16

[0038] Several refinements can be applied to the joint quantization/normalization procedure described above. The general technique of factoring the parameters into a mantissa and exponent forms the basis of these refinements.

[0039] The discussion above assumes all basis functions of the transform have an equal norm and are quantized identically. Some integer transforms have the property that different basis functions have different norms. The present invention technique has been generalized to support transforms having different norms by replacing the scalars A[qp] and B[qp] above by matrices A[qp][i][j] and B[qp][i][j]. These parameters are linked by a normalization relation of the form shown below, Equation 7, which is more general than the single relation shown in Equation 1.

Equation 7 Joint Quantization/normalization of Matrices

A[qp][i][j]·B[qp][i][j]=N[i][j]′

[0040] Following the method previously described, each element of each matrix is factored into a mantissa and an exponent term as illustrated in the equations below, Equation 8.

Equation 8 Factorization of Matrix Parameters

A[qp][i][j]=A _(mantissa) [qp][i][j]·2^(A) ^(_(exponent)) ^([qp][i][j]).

B[qp][i][j]=B _(mantissa) [qp][i][j]·2^(B) ^(_(exponent)) ^([qp][i][j]).

[0041] A large number of parameters are required to describe these quantization and dequantization parameters. Several structural relations can be used to reduce the number of free parameters. The quantizer growth is designed so that the values of A are halved after each period P at the same time the values of B are doubled maintaining the normalization relation. Additionally, the values of A_(exponent)[qp][i][] and B_(exponent)[qp][i][j] are independent of i, j and qp in the range [0,P−1]. This structure is summarized by structural equations, Equation 9. With this structure there are only two parameters A_(exponent)[0] and B_(exponent)[0].

Equation 9 Structure of Exponent Terms

A _(exponent) [qp][i][j]=A _(exponent)[0]−qP/P

B _(exponent) [qp][i][j]=B _(exponent)[0]+qp/P

[0042] A structure is also defined for the mantissa values. For each index pair (i,j), the mantissa values are periodic with period P. This is summarized by the structural equation, Equation 10. With this structure, there are P independent matrices for A_(mantissa) and P independent matrices for B_(mantissa) reducing memory requirements and adding structure to the calculations.

Equation 10 Structure of Mantissa Terms

A _(mantissa) [qp][i][j]=A _(mantissa) [qp%P][i][j]

B _(mantissa) [qp][i][j]=B _(mantissa) [qp%P][i][j]

[0043] The inverse transform may include integer division that requires rounding. In cases of interest the division is by a power of 2. The rounding error is reduced by designing the dequantization factors to be multiples of the same power of 2, giving no remainder following division.

[0044] Dequantization using the mantissa values B_(mantissa)[qp] gives dequantized values that are normalized differently depending upon qp. This must be compensated for following the inverse transform. A form of this calculation is shown in Equation 11.

Equation 11 Normalization of Inverse Transform I

K[i][j]=B _(mantissa) [qp%P][i][j]·Level[i][j]

X=(T ⁻¹ ·K·T)/2^((N-qP/P))

[0045] To eliminate the need for the inverse transform to compensate for this normalization difference, the dequantization operation is defined so that all dequantized values have the same normalization. The form of this calculation is shown in Equation 12.

Equation 12 Normalization of Inverse Transform II

K[i][j]=B _(mantissa) [qp%P][i][j]·2^(qp/P) ·Level[i][j]

X=(T ⁻¹ ·K·T)/2^(N)

[0046] An example follows that illustrates the present invention use of quantization matrices. The forward and inverse transforms defined in Equation 13 need a quantization matrix rather than a single scalar quantization value. Sample quantization and dequantization parameters are given. Equation 14 and 16, together with related calculations, illustrate the use of this invention. This example uses a period P=6. $\begin{matrix} {{T_{forward} = \begin{pmatrix} 1 & 1 & 1 & 1 \\ 2 & 1 & {- 1} & {- 2} \\ 1 & {- 1} & {- 1} & 1 \\ 1 & {- 2} & 2 & {- 1} \end{pmatrix}}{T_{reverse} = \begin{pmatrix} 2 & 2 & 2 & 1 \\ 2 & 1 & {- 2} & {- 2} \\ 2 & {- 2} & {- 2} & 2 \\ 2 & {- 1} & 2 & {- 1} \end{pmatrix}}} & \text{Equation~~13~~transforms} \\ {{{{{Q\lbrack m\rbrack}\lbrack i\rbrack}\lbrack j\rbrack} = {{M_{{m{.0}}\quad}{{for}\left( {i,j} \right)}} = \left\{ {\left( {0,0} \right),\left( {0,2} \right),\left( {2,0} \right),\left( {2,2} \right)} \right\}}}{{{{Q\lbrack m\rbrack}\lbrack i\rbrack}\lbrack j\rbrack} = {{M_{{m{.0}}\quad}{{for}\left( {i,j} \right)}} = \left\{ {\left( {1,1} \right),\left( {1,3} \right),\left( {3,1} \right),\left( {3,3} \right)} \right\}}}{{{{Q\lbrack m\rbrack}\lbrack i\rbrack}\lbrack j\rbrack} = {M_{m{.0}}\quad {otherwise}}}{M = \begin{bmatrix} 21844 & 8288 & 13108 \\ 18724 & 7625 & 11650 \\ 16384 & 6989 & 10486 \\ 14564 & 5992 & 9532 \\ 13107 & 5243 & 8066 \\ 11916 & 4660 & 7490 \end{bmatrix}}} & \text{Equation~~14~~quantization~~parameters} \\ {{{{{R\lbrack m\rbrack}\lbrack i\rbrack}\lbrack j\rbrack} = {{S_{{m{.0}}\quad}{{for}\left( {i,j} \right)}} = \left\{ {\left( {0,0} \right),\left( {0,2} \right),\left( {2,0} \right),\left( {2,2} \right)} \right\}}}{{{{R\lbrack m\rbrack}\lbrack i\rbrack}\lbrack j\rbrack} = {{S_{{m{.0}}\quad}{{for}\left( {i,j} \right)}} = \left\{ {\left( {1,1} \right),\left( {1,3} \right),\left( {3,1} \right),\left( {3,3} \right)} \right\}}}{{{{R\lbrack m\rbrack}\lbrack i\rbrack}\lbrack j\rbrack} = {S_{m{.0}}\quad {otherwise}}}{S = \begin{bmatrix} 6 & 10 & 8 \\ 7 & 11 & 9 \\ 8 & 12 & 10 \\ 9 & 14 & 11 \\ 10 & 16 & 13 \\ 11 & 18 & 14 \end{bmatrix}}} & \text{Equation~~16~~Dequantization~~parameters} \end{matrix}$

[0047] The description of the forward transformation and forward quantization, Equation 18, are given below assuming input is in X, quantization parameter QP.

Equation 17 Forward Transform

K=T _(forward) ·X·T _(forward) ^(T)

Equation 18 Forward Quantization

period=QP/6

phase=QP−6·period

Level[i][j]=(Q[phase][i][j]·K[i][j])/2^((17+period))

[0048] The description of dequantization, inverse transform, and normalization for this example is given below, Equation 19 and 20.

Equation 19 Dequantization

period=QP/6

phase=QP−6·period

K[i][j]=R[phase][i][j]·Level[i][j]19 2^(period)

Equation 20 IDCT and Normalization

X′=T _(reverse) ·K·T _(reverse) ^(T)

X″[i][j]=X′[i][j]/2⁷

[0049]FIG. 1 is a flowchart illustrating the present invention method for the quantization of a coefficient. Although this method is depicted as a sequence of numbered steps for clarity, no order should be inferred from the numbering unless explicitly stated. It should be understood that some of these steps may be skipped, performed in parallel, or performed without the requirement of maintaining a strict order of sequence. The methods start at Step 100. Step 102 supplies a coefficient K. Step 104 supplies a quantization parameter (QP). Step 106 forms a quantization value (L) from the coefficient K using a mantissa portion (Am)(QP)) and an exponential portion (x^(Ae(QP))). Typically, the exponential portion (x^(Ae(QP))) includes x being the value 2.

[0050] In some aspects of the method, forming a quantization value (L) from the coefficient K using a mantissa portion (Am)(QP)) and an exponential portion (x^(Ae(QP))) in Step 106 includes: L = K * A(QP) = K * Am(QP) * (2^(Ae(QP))).

[0051] Some aspects of the method include a further step. Step 108 normalizes the quantization value by 2^(N) as follows: ${Ln} = {\frac{L}{2^{N}} = {K*{Am}{\frac{({QP})}{2^{({N - {{Ae}{({QP})}}})}}.}}}$

[0052] In other aspects, forming a quantization value in Step 106 includes forming a set of recursive quantization factors with a period P, where A(QP+P)=A(QP)/x. Likewise, forming a set of recursive quantization factors includes forming recursive mantissa factors, where Am(QP)=Am(QP mod P). Then, forming a set of recursive quantization factors includes forming recursive exponential factors, where Ae(QP)=Ae(QP mod P)−QP/P.

[0053] In some aspects, forming a quantization value includes forming a set of recursive quantization factors with a period P, where A(QP+P)=A(QP)/2. In other aspects, forming a set of recursive quantization factors includes forming recursive mantissa factors, where P =6. Likewise, forming a set of recursive quantization factors includes forming recursive exponential factors, where P=6.

[0054] In some aspects of the method, supplying a coefficient K in Step 102 includes supplying a coefficient matrix K[i][j]. Then, forming a quantization value (L) from the coefficient matrix K[i][j] using a mantissa portion (Am)(QP) and an exponential portion (x^(Ae(QP))) in Step 106 includes forming a quantization value matrix (L[i][j]) using a mantissa portion matrix (Am(QP)[i][j]) and an exponential portion matrix (x^(Ae(QP)[i][j])). Likewise, forming a quantization value matrix (L[i][j]) using a mantissa portion matrix (Am(QP)[i][j]) and an exponential portion matrix (x^(Ae(QP)[i][j]) includes, for each particular value of QP, every element in the exponential portion matrix being the same value. Typically, every element in the exponential portion matrix is the same value for a period (P) of QP values, where Ae(QP)=Ae(P*(QP/P)).)

[0055] Some aspects of the method include a further step. Step 110 forms a dequantization value (X1) from the quantization value, using a mantissa portion (Bm)(QP)) and an exponential portion (x^(Be(QP))). Again, the exponential portion (X^(Be(QP))) typically includes x being the value 2.

[0056] In some aspects of the method, forming a dequantization value (X1) from the quantization value, using a mantissa portion (Bm)(QP)) and an exponential portion (2^(Be(QP))) includes: X1 = L * B(QP) = L * Bm(QP) * (2^(Be(QP))).

[0057] Other aspects of the method include a further step, Step 112, of denormalizing the quantization value by 2^(N) as follows: ${X1d} = {\frac{X1}{2^{N}} = {{X1}*{Bm}{\frac{({QP})}{2^{N}}.}}}$

[0058] In some aspects, forming a dequantization value in Step 110 includes forming a set of recursive dequantization factors with a period P, where B(QP+P)=x*B(QP). Then, forming a set of recursive dequantization factors includes forming recursive mantissa factors, where Bm(QP)=Bm(QP mod P). Further, forming a set of recursive dequantization factors includes forming recursive exponential factors, where Be(QP)=Be(QP mod P)+QP/P.

[0059] In some aspects, forming a set of recursive quantization factors with a period P includes the value of x being equal to 2, and forming recursive mantissa factors includes the value of P being equal to 6. Then, forming a set of recursive dequantization factors includes forming recursive exponential factors, where Be(QP)=Be(QP mod P)+QP/P.

[0060] In some aspects of the method, forming a dequantization value (X1), from the quantization value, using a mantissa portion (Bm)(QP)) and an exponential portion (x^(Be(QP))) in Step 110 includes forming a dequantization value matrix (X1[i][j]) using a mantissa portion matrix (Bm(QP)[i][j]) and an exponential portion matrix (x^(Be(QP)[i][j]). Likewise, forming a dequantization value matrix (X1[i][j]) using a mantissa portion matrix (Bm(QP) [i][j]) and an exponential portion matrix (x) ^(Be(QP)[i][j]) includes, for each particular value of QP, every element in the exponential portion matrix being the same value. In some aspects, every element in the exponential portion matrix is the same value for a period (P) of QP values, where Be(QP)=Be(P*(QP/P)).)

[0061] Another aspect of the invention includes a method for the dequantization of a coefficient. However, the process is essentially the same as Steps 110 and 112 above, and is not repeated in the interest of brevity.

[0062] A method for the quantization of a coefficient has been presented. An example is given illustrating a combined dequantization and normalization procedure applied to the H.26L video coding standard with a goal of reducing the bit-depth required at the decoder to 16 bits. The present invention concepts can also be used to meet other design goals within H.26L. In general, this invention has application to the combination of normalization and quantization calculations. Other variations and embodiments of the invention will occur to those skilled in the art. 

We claim:
 1. A method for the quantization of a coefficient, the method comprising: supplying a coefficient K; supplying a quantization parameter (QP); forming a quantization value (L) from the coefficient K using a mantissa portion (Am)(QP)) and an exponential portion (x^(Ae(QP))).
 2. The method of claim 1 wherein the exponential portion (x^(Ae(QP))) includes x being the value
 2. 3. The method of claim 2 wherein forming a quantization value (L) from the coefficient K using a mantissa portion (Am)(QP)) and an exponential portion (x^(Ae(QP))) includes: L = K * A(QP) = K * Am(QP) * (2^(Ae(QP))).


4. The method of claim 3 further comprising: normalizing the quantization value by 2^(N) as follows: ${Ln} = {\frac{L}{2^{N}} = {K*{Am}{\frac{({QP})}{2^{({N - {{Ae}{({QP})}}})}}.}}}$


5. The method of claim 1 wherein forming a quantization value includes forming a set of recursive quantization factors with a period P, where A(QP+P)=A(QP)/x.
 6. The method of claim 5 wherein forming a set of recursive quantization factors includes forming recursive mantissa factors, where Am(QP)=Am(QP mod P).
 7. The method of claim 5 forming a set of recursive quantization factors includes forming recursive exponential factors, where Ae(QP)=Ae(QP mod P)−QP/P.
 8. The method of claim 4 wherein forming a quantization value includes forming a set of recursive quantization factors with a period P, where A(QP+P)=A(QP)/2.
 9. The method of claim 6 wherein forming a set of recursive quantization factors includes forming recursive mantissa factors, where P=6.
 10. The method of claim 7 forming a set of recursive quantization factors includes forming recursive exponential factors, where P=6.
 11. The method of claim 1 wherein supplying a coefficient K includes supplying a coefficient matrix K[i][j]; wherein forming a quantization value (L) from the coefficient matrix K[i][j] using a mantissa portion (Am)(QP) and an exponential portion (x^(Ae(QP))) includes forming a quantization value matrix (L[i][j]) using a mantissa portion matrix (Am(QP)[i][j]) and an exponential portion matrix (x^(Ae(QP)[i][j]).)
 12. The method of claim 11 wherein forming a quantization value matrix (L[i][j]) using a mantissa portion matrix (Am(QP)[i][j]) and an exponential portion matrix (x^(Ae(QP)[i][j]) includes, for each particular value of QP, every element in the exponential portion matrix being the same value.)
 13. The method of claim 12 wherein every element in the exponential portion matrix is the same value for a period (P) of QP values, where Ae(QP)=Ae(P*(QP/P)).
 14. The method of claim 1 further comprising: forming a dequantization value (X1) from the quantization value, using a mantissa portion (Bm)(QP)) and an exponential portion (x^(Be(QP))).
 15. The method of claim 14 wherein the exponential portion (x^(Be(QP))) includes x being the value
 2. 16. The method of claim 15 wherein forming a dequantization value (X1) from the quantization value, using a mantissa portion (Bm)(QP)) and an exponential portion (2^(Be(QP))) includes: $\begin{matrix} {{X1} = {L*{B({QP})}}} \\ {= {L*{{Bm}({QP})}*{\left( 2^{{Be}{({QP})}} \right).}}} \end{matrix}$


17. The method of claim 16 further comprising: denormalizing the quantization value by 2^(N) as follows: $\begin{matrix} {{X1d} = {{X1}/2^{N}}} \\ {= {{X1}*{{{Bm}({QP})}/{2^{N}.}}}} \end{matrix}$


18. The method of claim 14 wherein forming a dequantization value includes forming a set of recursive dequantization factors with a period P, where B(QP+P)=x*B(QP).
 19. The method of claim 18 wherein forming a set of recursive dequantization factors includes forming recursive mantissa factors, where Bm(QP)=Bm(QP mod P).
 20. The method of claim 19 forming a set of recursive dequantization factors includes forming recursive exponential factors, where Be(QP)=Be(QP mod P)+QP/P.
 21. The method of claim 18 wherein forming a set of recursive quantization factors with a period P includes the value of x being equal to
 2. 22. The method of claim 19 wherein forming recursive mantissa factors includes the value of P being equal to
 6. 23. The method of claim 22 forming a set of recursive dequantization factors includes forming recursive exponential factors, where Be(QP)=Be(QP mod P)+QP/P.
 24. The method of claim 14 wherein forming a dequantization value (X1) from the quantization value, using a mantissa portion (Bm)(QP)) and an exponential portion (x^(Be(QP))) includes forming a dequantization value matrix (X1[i][j]) using a mantissa portion matrix (Bm(QP)[i][j]) and an exponential portion matrix (x^(Be(QP)[i][j])).
 25. The method of claim 24 wherein forming a dequantization value matrix (X1[i][j]) using a mantissa portion matrix (Bm(QP)[i][j]) and an exponential portion matrix (x^(Be(QP)[i][j])) includes, for each particular value of QP, every element in the exponential portion matrix being the same value.
 26. The method of claim 23 wherein every element in the exponential portion matrix is the same value for a period (P) of QP values, where Be(QP)=Be(P*(QP/P)).
 27. A method for the dequantization of a coefficient, the method comprising: receiving a quantization value; forming a dequantization value (X1) from the quantization value, using a mantissa portion (Bm)(QP)) and an exponential portion (x^(Be(QP))).
 28. The method of claim 27 wherein the exponential portion (x^(Be(QP))) includes x being the value
 2. 29. The method of claim 28 wherein forming a dequantization value (X1) from the quantization value, using a mantissa portion (Bm)(QP)) and an exponential portion (2^(Be(QP))) includes: $\begin{matrix} {{X1} = {L*{B({QP})}}} \\ {= {L*{{Bm}({QP})}*{\left( 2^{{Be}{({QP})}} \right).}}} \end{matrix}$


30. The method of claim 29 wherein receiving the quantization value includes received a normalized quantization value; and, the method further comprising: denormalizing the quantization value by 2^(N) as follows: $\begin{matrix} {{X1d} = {{X1}/2^{N}}} \\ {= {{X1}*{{{Bm}({QP})}/{2^{N}.}}}} \end{matrix}$


31. The method of claim 27 wherein forming a dequantization value includes forming a set of recursive dequantization factors with a period P, where B(QP+P)=x*B(QP).
 32. The method of claim 31 wherein forming a set of recursive dequantization factors includes forming recursive mantissa factors, where Bm(QP)=Bm(QP mod P).
 33. The method of claim 32 forming a set of recursive dequantization factors includes forming recursive exponential factors, where Be(QP)=Be(QP mod P)+QP/P.
 34. The method of claim 31 wherein forming a set of recursive quantization factors with a period P includes the value of x being equal to
 2. 35. The method of claim 32 wherein forming recursive mantissa factors includes the value of P being equal to
 6. 36. The method of claim 35 forming a set of recursive dequantization factors includes forming recursive exponential factors, where Be(QP)=Be(QP mod P)+QP/P.
 37. The method of claim 27 wherein forming a dequantization value (X1) from the quantization value, using a mantissa portion (Bm)(QP)) and an exponential portion (x^(Be(QP))) includes forming a dequantization value matrix (X1[i][j]) using a mantissa portion matrix (Bm(QP)[i][j]) and an exponential portion matrix (x^(Be(QP)[i][j])).
 38. The method of claim 37 wherein forming a dequantization value matrix (X1[i][j]) using a mantissa portion matrix (Bm(QP)[i][j]) and an exponential portion matrix (x^(Be(QP)[i][j])) includes, for each particular value of QP, every element in the exponential portion matrix being the same value.
 39. The method of claim 36 wherein every element in the exponential portion matrix is the same value for a period (P) of QP values, where Be(QP)=Be(P*(QP/P)). 